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Journal of the Korean Physical Society, Vol. 59, No. 2, August 2011, pp. 855∼858
The Theoretical Calculation of Cross Section and Spectrum for n+238 U
Reaction up to 150 MeV
Yinlu Han,∗ Yongli Xu, Haiying Liang, Hairui Guo and Qingbiao Shen
China Nuclear Data Center, China Institute of Atomic Energy, Beijing 102413, China
Chonghai Cai
Department of Physics, Nankai University, Tianjin 300071, China
(Received 26 April 2010)
The fission cross sections, the double differential cross section and the energy spectra of neutron,
proton, deuteron, triton, and alpha-particle emission, the prompt fission neutron spectra for n+238 U
reaction are consistently calculated and analyzed with nuclear reaction theoretical models in the
En ≤ 150 MeV energy range. Theoretical calculations are compared with recent experimental data
and other evaluated data.
PACS numbers: 25.40.-h, 28.20.-v, 25.28.Ec
Keywords: Nuclear reaction theoretical models, Neutron-induced fission reactions
DOI: 10.3938/jkps.59.855
spectra, the angle-integrated spectra and the double differential cross sections of neutron, proton, deuteron, triton, and alpha-particle emission for n+238 U reaction are
calculated using the optical model, the unified HauserFeshbach and exciton model which included the improved Iwamoto-Harada model, the Bohr-Wheeler theory, the distorted wave Born approximation and recent
experimental data for the incident neutron energy region
En ≤ 150 MeV. Based on the analysis of reaction cross
sections, the energy spectra and the double differential
cross sections for neutron, proton, deuteron, triton and
alpha-particle emission are analyzed and compared with
experimental data.
I. INTRODUCTION
Neutron-induced reactions on uranium isotopes in the
energy range below 150 MeV are of fundamental importance in the field of nuclear energy and nuclear transmutation [1]. For example, these interactions dominate
neutron generation and neutron transport in accelerator supported nuclear reactors, such as the proposed
accelerator driven system of Ref. 2. Knowledge of accurate neutron-induced fission cross sections is crucially
important for the design of various reactor systems. On
the other hand, since neutron, proton, deuteron, triton,
and alpha-particle emission double differential cross section and spectra provide a complementary information
on prompt fission neutrons and nuclear reaction mechanisms, theoretical model calculation can obtain more information about nucleus structure and nuclear reaction.
Furthermore, accurate modelling of the reaction mechanism is important for designing the next generation of
nuclear reactors.
Recently, several new experimental data of n+238 U
reaction have been reported for the total, fission and
neutron emission double differential cross sections and
energy spectra. The new experimental data provide
complementary information on nucleon induced light
charged particle emission and offer a larger base for
testing the nuclear models. The reproduction of light
charged particles properties appears as one of the most
challenging problems.
In the present work, all reaction cross sections, number of neutron per fission, the prompt fission neutron
∗ E-mail:
II. THEORETICAL MODELS AND
CALCULATED RESULTS
The optical model is used to describe measured
neutron-induced total, nonelastic, elastic cross section
and elastic scattering angular distributions, and calculate the transmission coefficient of the compound nucleus and the preequilibrium emission process. The optical model potentials considered here are Woods-Saxon
[3] form for the real part, Woods-Saxon and derivative
Woods-Saxon form for the imaginary parts corresponding to the volume and surface absorptions respectively,
and the Thomas form for the spin-orbit part.
The unified Hauser-Feshbach and exciton model [4] is
used to describe the nuclear reaction equilibrium and
preequilibrium decay processes. The preequilibrium statistical theory based on the angular momentum dependent exciton model, the evaporation models and HauserFeshbach theory with width fluctuation correction, and
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Journal of the Korean Physical Society, Vol. 59, No. 2, August 2011
intranuclear cascade model are used to describe the nuclear reaction preequilibrium and equilibrium decay processes. The improved Iwamoto-Harada model [5, 6] are
used to describe the composite particle emission in compound nucleus.
Fission is included as a decay channel, that is, a fission competitive width can be estimated at every step
of the cascades. Fifteen uncoupled fission barriers are
used to represent the fission system and describe (n, f ),
(n, nf ), ··· , (n, 15nf ) channels, respectively. At each
barrier a series of transition states characterized by excitation energy above the barrier, spin and parity can
be constructed. At higher energies the discrete transition states are replaced by a continuum of such states,
using the Gilbert-Cameron level density [7] prescription
and appropriate level density enhancement factors. The
Bohr-Wheeler theory [8,9] is used in transmission coefficients computed at each barrier.
The double differential cross section can be calculated
by generalized master equation to get the angular momentum dependent lifetime with the Legendre expansion
form. In order to simplify the calculations, the angular dependent formula form of Kalbach phenomenological approach [10,11] above incident 20 MeV is used in
present calculation of the double differential cross sections for neutron, proton, deuteron, triton and alphaparticle emission.
The UNF code [12] is used at incident neutron energies
below 20 MeV. The nuclear reaction models code MEND
[13] is used in the energy range up to 150 MeV. The neutron and proton optical model potential parameters [14]
are obtained from experimental data of total, nonelastic cross sections and elastic scattering angular distributions. The optical potential parameters for deuteron
[15] are obtained and used as triton optical potential parameters. The optical potential parameters for helium
and alpha particles are taken from Greenlees’s results
[3]. The code DWUCK4 [16] of the distorted wave Born
approximation theory is used to pre-calculate the direct
inelastic scattering cross sections and angular distributions of discrete levels.
All reaction cross section, the energy spectrum of
neutron, proton, deuteron, triton and alpha emission
for n+238 U reaction are calculated. The calculated results of total, nonelastic and elastic scattering cross sections, elastic scattering angular distributions and inelastic scattering angular distributions of discrete level are
in good agreement with experimental data as shown in
Ref. 14. The fission cross section obtained from theoretical calculations agree with the experimental data [17],
and larger than those of experimental data [18] as shown
in Fig. 1. The experimental data for (n, 2n) and (n, 3n)
reaction cross sections were given in different laboratories, and there are significant differences. The calculated results for (n, 2n) reaction cross sections as shown
in Fig. 2 are in good agreement with some experimental
data and the calculated results for (n, 3n) reaction cross
sections are basically in agreement with the experimen-
Fig. 1. Calculated fission cross sections (solid line) compared with experimental data.
Fig. 2. Calculated (n, 2n) reaction cross sections (solid
line) compared with experimental data.
Fig. 3. Calculated double differential cross sections of neutron emission compared with experimental data.
The Theoretical Calculation of Cross Section and Spectrum for n+238 U Reaction· · · – Yinlu Han et al.
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Fig. 4. Calculated double differential cross sections of neutron emission compared with experimental data.
Fig. 7. Calculated double differential cross sections of
deuteron emission compared with experimental data.
Fig. 5. Calculated double differential cross sections of neutron emission compared with experimental data.
Fig. 8. Calculated double differential cross sections of triton emission compared with experimental data.
Fig. 6. Calculated double differential cross sections of proton emission compared with experimental data.
Fig. 9. Calculated double differential cross sections of alpha emission compared with experimental data.
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Journal of the Korean Physical Society, Vol. 59, No. 2, August 2011
generally observed for different reaction cross sections.
The theoretical models provide the good description
of the shapes and magnitude of the double differential
cross section of neutrons, protons, deuterons, tritons
and alphas emission for some emission angles and energies. All of the present results have been transformed
into ENDF formatted data files for application.
ACKNOWLEDGMENTS
Fig. 10. Calculated energy spectra of proton, deuteron,
triton and alpha emission compared with experimental data.
tal data. The calculated results of (n, 4n), (n, 5n), ···
, (n, 10n) reaction cross sections are physically reasonable. The double differential cross sections of neutron
emission are compared with experimental data [19, 20]
at incident neutron energies 1.2, 6.1, and 18.0 MeV as
shown in Figs. 3 to 5. The calculated results are in good
agreement with experimental data. Figures show some
fluctuations in the calculated results, which are from discrete level contribution. The calculated results are from
the contribution of the fission channel when emission
neutron energy is larger than incident neutron energy.
The calculated results of double differential cross sections of proton, deuteron, triton and alpha emission are
compared with experimental data [21] at incident neutron energy 49.0 MeV as shown in Figs. 6 to 9. The
shape and magnitude of calculated results curve for all
of emission angles are in agreement with those of experimental data. The calculated results of energy spectrum
of proton, deuteron, triton and alpha emission are compared with experimental data [21] at incident neutron
energy 41.0 MeV as shown in Fig. 10. The magnitude
and shape of calculated results curve are in agreement
with those of experimental data.
III. CONCLUSION
All cross sections, angular distributions, the energy
spectra and double differential cross sections are consistently calculated using nuclear theory models for
n+238 U reaction at incident neutron energies from 0.1 to
150 MeV. The comparison and analysis of experimental
data and calculated results show good agreement are
This work is part of National Basic Research Program
of China (973 Program), and is supported by the China
Ministry of Science and Technology under Contract No.
2007CB209903. This work is a part of IAEA Coordinated Research Projects (CRPs) on Analytical and Experimental Benchmark Analyses of Accelerator Driven
Systems (ADS) under Contract No. 13390/R2, and Minor Actinides Neutron Cross Section Data for Closed
Fuel Reactor Concepts under Contract No. 14383/R1.
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